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Architectural Engineer need help with pump question

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I have a question in my sample exam that is probably straighforward, but I was hoping someone could clarify:

Q: A 6" pump operating at 1800 rpm discharges 1800 gpm of cold water (S.G. = 1) against an 80 foot head at 60% efficiency. A dynamically similar 8" pump operating at 1170 rpm is considered as a replacement. The total head that can be expected from the new pump is most nearly I am a Gigantic DoucheBag

A: 60.09 ft

In the solutions they show the work, but don't explain why they did what they did: head = (8/6 * 1170/1800)^2 * 80 = 60.09

It looks like they just did proportions? What is the base equation they started with?

Thanks,

- Dave

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My first thought would be Hazen-WIlliams or Darcy Weisbach.. Let me take a look at this.

Darcy is H = F*(L/D)*(V^2/(2g))

I think it is safe to assume since they said the second pump is a replacement that vertical component of the total head is irrelevant. I would assume this is a friction head loss question.

I might be wrong though ... Let me sleep on this one.

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I believe they used the pump affinity laws to solve the problem. Engineering toolbox has a pretty good example.

thanks

Kelly

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These look like proportions because they are. You should brush up on Affinity Laws, and Pump Similarity. Your problem is a direct translation from Pump Similarity.

"The performance of one pump can be used to predict the performance of a dynamically similar (homologous) pump. This can be done by using Eqs. 18.48 through 18.53."

The first equation, 18.48, Is where the work they show comes from.

n1, D1, h1, n2, D2 are knowns, solve for h2

Edit: Sorry, forgot to reference this is from the MERM, ch. 18-25. Also, Example prob. 18.11 is almost the same situation.

Edited by pbrme

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